Metallography—A Practical Tool for Correlating the Structure and Properties of Materials 9780803105102, 080310510X

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METALLQGRAPHY- A PRACTICAL TOOL FOR CORRELATING THE STRUCTURE AND PROPERTIES OF MATERIALS

A symposium presented at the Seventy-sixth Annual Meeting AMERICAN SOCIETY FOR TESTING AND MATERIALS Philadelphia, Pa., 25-26 June 1973

ASTM SPECIAL TECHNICAL PUBLICATION 557 Halle Abrams and G. N. Maniar, symposium cochairmen

04-557000-28

AMERICAN SOCIETY FOR TESTING AND MATERIALS 1916 Race Street, Philadelphia, Pa. 19103

9by AMERICAN SOCIETY for TESTING and MATERIALS 1974

Library of Congress Catalog Card Number: 74-77096

NOTE The Society is not responsible, as a body, for the statements and opinions advanced in this publication.

Printed in Tallahassee, Fla. July 1974 Second Printing May 1981 Baltimore, Md.

Foreword The symposium on Metallography-A Practical Tool for Correlating the Structure and Properties of Materials, was given at the Seventy-sixth Annual Meeting of the American Society for Testing and Materials held in Philadelphia, Pa., 25-26 June 1973. Committee E-4 on Metallography sponsored the symposium. Halle Abrams, Bethlehem Steel Corporation, and G.N. Maniar, Carpenter Technology Corporation, presided as symposium cochairmen.

Related ASTM Publications

Electron Beam Microanalysis, STP 506 (1972), $3.75 (04-506000-28) Stereology and Quantitative Metallography, STP 504 (1972), $9.75 (04-504000-28) Manual on Electron Metallography, STP 547 (1973), $5.25 (04-547000-28)

Contents Introduction

1

Structure-Sensitive Properties of Materials Disclosed by a Combination of X-Ray Topography, X-Ray Diffraction Analysis, and Electron Microscopy Methods--SIGMUND WEISSMANN

4

Combination Method Based on X-Ray Divergent Beam Techniques Contribution of the Back-Reflection Patterns to Precision Measurements of Interplanar Spacings Computation of Stress-Strain Configuration of Strained Crystal; Applications and Limitations X-Ray Line Profile Analysis. Selected Area X-Ray Topography Based on Transmission Patterns Lattice Distortions and Fracture in Brittle Crystals Disclosed by Anomalous Transmission of X-Rays (Borrmann Effect) Instrumentation of X-Ray Divergent Beam Combination Method Study of Fracture Mechanism in Crystals by a Combination Method Based on X-Ray Pendello'sung Fringes, Double-Crystal Diffractometry, TEM, and SEM Discussion-Interplay of Component Techniques in Combination Methods Conclusions

20 21

X-Ray Diffraction-A Versatile, Quantitative, and Rapid Technique of Metallography--LEO ZWELL

23

Specimen Preparation Elemental Analysis Phase Identification Other Structural Characteristics Conclusion

The Use of Hot-Stage Microscopy in the Study of Phase Transformations-a. L. BRAMFITT,A. O. BENSCOTER,J. R. KILPATRICK,AND A. a. MARDER Experimental Technique Heating Stage Applications

Examination of Materials by Coherent Light Techniques-R. J. SCHAEFER, J. A. BLODGETT,AND M. E. GLICKSMAN

5 6 7 8 10 14

16

24 25 29 34 40

43 43 44 54

71

Coherence Optical Transforms Holography Optical Correlation Summary

The Electron Microprobe as a Metallographic Tool-J. I. GOLDSTEIN Electron Microprobe Elemental Analysis Scanning Electron Probe Characterization of Phases EMP Analysis of Phases Extension of Instrument Capability

Transmission Electron Microscopy in Materials Research-M. G. H. WELLS AND J. M. CAPENOS Instrument Design Improvements New Observation Techniques Use of TEM in Structure-Property Relationships

72 72 75 84 84 86 87 94 103 108 115 120

137 141 141 144

High Voltage Electron Metallography-Achievements and ProspectsA . S Z I R M A E A N D R. M. F I S H E R

Characteristics of High Voltage Microscopy Applications Future Developments

169 171 184 196

Microstructure Approach to Property Optimization in Wrought Superalloys--D. R. MUZYKAAND G. N. MANIAR 198 Alloys Primary Manufacturing Steps Phases in Wrought Superalloys and Metallographic Techniques Microstructures and Properties Recent Developments Micrograin Processing Structure Control Heat Treating Minigrain Processing Thermomechanical Processing Summary

199 201 203 205 206 206 208 210 212 217

Phase Separation as a Technique for the Characterization of Superalloys - - 0 . H. KRIEGE 220 Specific Techniques for Phase Separation Analysis of Separated Phases Application of Phase Separation to Metallurgical Studies Summary

221 225 227 233

STP557-EB/Jul. 1974

Introduction

In the last several years the characterization of materials by metallographic techniques has been paralleled by a remarkable improvement in material capabilities. The ability to measure and characterize those material parameters that provide improved mechanical and physical properties has led directly to the development of new and better materials. Well known metallographic techniques such as hot-stage microscopy, transmission electron microscopy (TEM), and X-ray analysis, as well as the more recent techniques of scanning electron microscopy (SEM) and automatic quantitative metallography have provided the means to measure, characterize, statistically interpret, and, finally, predict the properties of materials. The successful correlation of the structure and properties of materials, whether on a theoretical or empirical level, has been one of the primary forces in the current materials revolution. Accordingly, the objective of this symposium was to present both review and original papers that demonstrated, on a practical level, the application of an expanded range of metallographic techniques to the measurement, characterization, statistical interpretation, and prediction of the behavior of materials. The papers presented have been prepared by authorities in their fields and include almost all phases of modern metallographic techniques. The opening session dealt with electron optical metallography covering the areas of electron microprobe analysis, SEM, and high voltage and conventional electron metallography. The second session covered hot-stage microscopy, microhardness techniques, and the new laser techniques of evaluating metallographic structures. The final session included a complete review of the techniques and applications of X-ray metallography and two application papers in the field of superalloys. This special technical publication includes all the papers presented at the symposium, with the exception of the SEN and microhardness papers, which are not included due to publication deadlines. Professor Weissman's paper is an excellent and concise summary of the X-ray metallographic techniques that he and his colleagues have developed to a high degree of sophistication over the past several years. In his paper, he describes various applications where combination X-ray methods are used to correlate lattice defects with structure-sensitive properties. In particular, his description of the use of X-ray Pendell6sung fringes to analyze the distribu-

Copyright 91974 by ASTMIntemational

www.astm.org

2

METALLOGRAPHY

tion of microplastic and elastic strains in crack propagation would be of special interest to researchers working with low dislocation-density materials. In contrast to the more specialized techniques discussed by Weissman, Zwell's paper deals with practical applications of the more common X-ray metaUographic techniques such as phase identification, residual-stress analysis, and texture determinations. The author demonstrates the usefulness of these techniques in failure analysis as well as in the development of new alloys. In their paper, Bramfitt et aL, summarize the experimental techniques used in hot-stage light microscopy and the application of these techniques to the study of ferrous transformations. The paper provides a description of all the transformations occurring in low-alloy steels and includes an excellent bibliography. Of particular merit is the authors' work on the austenite to pearlite transformation emphasizing the advantage of in situ measurements on a single specimen to determine pearlite-nodule growth rates and transformation kinetics. Another innovative technique in light microscopy is described by Schaefer et aL Their paper discusses the basic concepts involved in the analysis of metallographic structures using optical transforms, holography, and other coherent-light methods. For the materials scientists, the most useful applications of holography employ interferometry to study transient events that occur at unpredictable locations, for example, the solidification of transparent analogs of metals. The following three papers relate to the use of electron optics for characterizing and correlating the structure and properties of materials. In his paper, Professor Goldstein discusses the resolution and types of information that can be obtained from the various X-ray, secondary electron, and backscattered electron signals measured in the electron microprobe. The paper demonstrates the versatility of the microprobe as a metallurgical tool in the characterization of phases, diffusion studies, trace-element analysis, and quantitative metallography. The paper also contains an up-to-date and extensive bibliography. The review paper by Wells and Capenos describes applications of TEM in materials research. In covering selective papers from the literature, the authors provide several practical examples of the role of TEM in the study and understanding of materials system. The scope of applications of electron metallography has been expanded considerably with the advent of high-voltage instruments capable of operating at 1 MeV or more. In the area of high voltage electron metallography, the contributions of Szirmae and Fisher are well known, and their present paper presents a broad review of their work and a look toward the future of high voltage electron metallography (HVEM). The paper by Muzyka and Maniar demonstrates the application of various metaUography methods in optimizing properties of superalloys on the basis of a microstructural approach. The authors illustrate the value of microstructural studies in conjunction with phase relationships in improving hot working, heat-treat response, and the property optimization of iron and iron.nickel base superalloys. The contribution of analytical chemistry in support of microstructure studies is exemplified by Kriege's paper on phase separation as a

INTRODUCTION

3

technique for the characterization of superalloys. Although the paper deals with superalloys, the technique is equally applicable to other material systems. These introductory comments on the papers contained in this volume illustrate the significant role that metallography plays in the development and characterization of materials. It was our objective in organizing this symposium to show, through both original studies and state-of-the-art reviews, how the metaUographic disciplines within the scope of Committee E-4 on MetaUography validate the premise that metallography is a practical tool for correlating the structure and properties of materials. We hope that this publication has contributed to the achievement of our objective. The American Society for Testing and Materials (ASTM) and the program chairmen wish to thank the authors for their excellent contributions to the symposium and this volume.

Halle Abrams Homer Research Laboratories, Bethlehem Steel Corp., Bethlehem, Pa. 18015; symposium

cochairman.

Gunvant N. Maniar Manager, Research and Development Center, Carpenter Technology Corp., Reading, Pa. 19603; symposium coehairman.

Sigmund Weissmann ~

Structure- Sensitive Propertiesof Materials Disclosed by a Combinationof X- Ray Topography,X-Ray Diffraction Analysis, and Electron Microscopy Methods REFERENCE: Weissmann, Sigmun~l, "Slxucture-Sensitive Properties of Materials Disclosed by a Combination of X-Ray Topography, X-Ray Diffraction Analysis, and Electron Microscopy Methods," Metallography-A Practical Tool for Correlating the Structure and Properties of Materials, ASTM STP 557, American Society for Testing and Materials, 1974, pp. 4-22. ABSTRACT: To establish a significant correlation between lattice defects and structure-sensitive properties it is frequently desirable to combine various methods of structural analysis which provide supplementary information and have a synergistic effect on the course of study. Such combination methods have been developed in this laboratory. They comprise: (a) selected area X-ray topography, (b) X-ray line profile analysis, (e) anomalous X-ray transmission topography, (d) X-ray double-crystal diffractometry, (e) analysis of plastic and elastic strain distribution by disturbance~of X-ray pendeUiisung fringes (PF), (f) transmission electron microscopy (TEM) of dislocation structure in selected areas of the specimen, and (g) scanning electron microscopy (SEM) of the specimen. Examples of the application of these combination methods are presented that include the tensile and compressive deformation of beryllium crystals, the deformation and fracture of germanium and silicon crystals, and the elucidation of the distribution of microplastic and elastic strains in crack propagation. KEY WORDS: X-ray analysis, transmission, scanning, electron microscopy, deformation, fractures (materials), germanium, silicon, beryllium, plastic deformation, elastic properties Many important properties of materials are structure-sensitive, and often a relatively small number of lattice defects have a disproportionately large effect on the properties. Of particular interest from scientific and technological viewpoints alike are the mechanical properties. To establish a significant correlation between lattice defects and mechanical properties it is frequently desirable to combine various methods of structural analysis which provide supplementary information and have a synergistic effect on the course of study. Such combination methods have been developed in the author's laboratory over a span of nearly two decades in response to challenging problems in materials science. Although some component parts of structural analysis have been treated individually in previous publications, an attempt will be made in this paper, spurred by new developments, to synthesize them all into powerful combination methods. Particular emphasis will be placed on these new developments and on the synergistic interplay of the component techniques. Exam1 Professor, Materials Research Laboratory, College of Engineering, Rutgers University, New Brunswick, N.J. 08903.

Copyright 91974 by ASTM Intemational

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WEISSMANN ON STRUCTURE-SENSITIVE PROPERTIES

5

pies will be presented which are relevant to problems of deformation and fracture of materials and which may serve to demonstrate the general usefulness of these methods. Since the principal aim of this paper is to show how the component techniques of the combination methods complement each other and to demonstrate what overall results one may expect, the reader will be frequently referred to previous publications for detailed technical information. Combination Method Based on X-Ray Divergent Beam Techniques About two decades ago the study of lattice defects of single crystals was virtually confined to academic investigations only, but, starting with the development of transistor materials and spurred in recent years by the increased interest in ferroelectric, piezoelectric, and magnetic device materials, such studies have become also increasingly important to applied technology. The X-ray diffraction method using a divergent beam as the X-ray source is well suited to provide the basis for a quantitative strain analysis of single crystals [1] 2 and to offer a visualization of the defect structure by X-ray topography and by transmission electron microscopy (TEM). The divergent beam method utilizes a long, horizontal X-ray tube, shown schematically in Fig. I. An electron beam originating from an electron gun is Back

--

a~

Reflectlotl

Specimen

.~

Single Crystol

Forward

Reflection

,.-~'.,

FIG. 1-Schematic representation of the generation of pseudo-Kossel pattern by the divergent beam method. 2 The italic numbers in brackets refer to the list of references appended to this paper.

6

METALLOGRAPHY

focused by means of an electromagnetic lens onto the tip of the vacuum-tight tube dosed by a thin metal foil. Since the metal foil is bombarded by the electron beam, it functions as an X-ray target. By operating the tube at a suitable voltage, an X-ray beam composed mainly of characteristic radiation emerges from the tip of the tube, exhibiting a divergence of nearly 180 deg of arc. At the point of emergence the beam size is about 10/am in diameter. When this beam impinges on the specimen, which is placed close to the tip of the tube, diffraction patterns of the characteristic spectrum in transmission, as well as in back reflection, may be recorded (Fig. 1). Since the X-ray source is located outside of the specimen, the conic patterns thus obtained are referred to frequently as pseudo-Kossel patterns to distinguish them from the true Kossel patterns, which are obtained by generating the X-ray source inside the crystal. The method offers the unique advantage that various (hkl) planes, even sets of planes of a form, which satisfy the Bragg condition for reflection of the impinging divergent beam, will be recorded as separate reflections without the necessity of rotating the crystal. As shown in Fig. 1, the diffraction cones intersect the film in ellipse-like figures in the back-reflection region, while in transmission two types of patterns are obtained, namely, the diffraction conic and the deficiency conic patterns. Both types of the transmission pattern emanate from the same irradiated small crystal volume transversed by the beam. It is the combined application of the back-reflection and transmission arrangement in the divergent beam method which jointly with TEM forms the basis of the first combination method of structural analysis to be discussed presently.

Contribution of the Back-Reflection Patterns to Precision Measurements of Interplanar Spacings [2] The back-reflection pseudo-Kossel pattern forms the principal basis for precision measurements of the interplanar spacings of the crystal. Since the exposure times of the back-reflection pattern are very short, varying from seconds to a few minutes depending on the diffracting power of the material, the elliptical pattern can be repeated several times by varying, with the aid of precision spacers, the film positions in a controlled manner. It will be seen from Fig. 1 that if the consecutive film position is c, the slopes m~ and m2 can be determined from the relationship m i = ~ / c = tan(t~ +/3)

(1)

rn2 = ~/c = tan(~ - ~)

(2)

where ~ is the semiapex angle of the incident X-ray cone equal to ~r[2 - 0, 0 being the Bragg angle, and fl is the angle subtended by the normal of the reflecting (hkl) plane and the axis of the X-ray tube. Using a multiple exposure technique such as that shown in Fig. 2, the slope parameters ml and m2 of the diffracted rays are obtained by a method of

WEISSMANN ON STRUCTURE-SENSITIVE PROPERTIES

7

FIG. 2-Multiple exposure back-reflection divergent beam photograph of berylliumoxygen. (Courtesy of Dr. D.K. Smith, Pennsylvania State University.} least squares. The simultaneous solution of Eqs 1 and 2 yields ~ and hence the corresponding Bragg angle 0. Subsequent substitution in the Bragg equation yields the corresponding d value of the interplanar spacing. A computer program was written to expedite the repeated computation of d spacings. The input to this program was: film coordinates Yi, which are the intersections of the major axis with the ellipse, such as points P and R in Fig. 1; spacing coordinates Xi, which represent the distance of the film from a fixed origin O; film shrinkage factor and wavelength used. The output was: d spacings and their corresponding standard errors [2].

Computation of Stress-Strain Configuration of Strained Crystal; Applications and Limitations The output of d-spacing computations of the various (hkl) reflections may now be used for the computation of a complete stress-strain analysis of the crystal [1,3]. If the crystal contains homogeneous, residual strains, then the changes in the interatomic spacings Adhk l induced by the strains are manifested sensitively by changes in the parameters of the ellipses and hence in the

8

METALLOGRAPHY

observed d spacings. If the strained crystal is sampled from many different directions, a collection of ,~l[d values is obtained which characterizes the strain distribution. The strain analysis which was developed recognizes the Ad[d values to represent elements of an average strain tensor and by measuring more than six independent (hkl) reflections the normal matrix equation is constructed and the average tensor < T > determined. The principal strains el 11, e222, e333 are obtained as the eigen values of the matrix solution. A computer program was written which uses as its input data the collection of Ad[d values, and supplies as output data the normal principal strains e111, 6222, e333 and their crystallographic directions [1]. If the elastic constants of the crystal are known, the complete stress-strain configuration is obtained [3,4]. Thus, the maximum magnitude and the direction of the shearing strain on a given set of crystallographic planes are obtained, and the set of crystallographic planes on which the maximum value of the shearing maxima occurs can also be determined. The stress-strain analysis based on the back-reflection divergent beam method has been successfully performed for cases where the strain inhomogeneities in the crystal were very small compared to the residual, homogeneous elastic strains. Examples can be found in: (a) strain configuration of precipitation-hardened aluminum-copper crystals where the Guinier-Preston zones of the semicoherent 0 'precipitates exert large, overall homogeneous strains in the matrix [1], (b) strains induced in the cubic matrix of copper-gold crystals by order transformation to tetragonal copper-gold I [3], (c) strains induced in oxidized a-titanium crystals by the ordering of oxygen atoms [6], and (d) strain distribution generated during the early stages of neutronirradiated quartz crystals [5]. It has been shown that the stress-strain analysis is not applicable to mechanically deformed crystals because the plastic strain inhomogeneities, caused by the induced dislocation structure, are large and vary from area to area [7]. Consequently, a representative sampling of the strain distribution cannot be obtained if the Ad/d values are being gathered from the back-reflection divergent beam pattern. Local strain inhomogeneities caused by mechanical deformation can be determined, however, with the aid of divergent beam patterns taken in transmission and the basis of such analysis will be presently described. X-Ray Line Profile Analysis. Selected Area X-Ray Topography Based on Transmission Patterns [8-11 ] It may be seen with the aid of Fig. 1 that in transmission the reflection cones (also referred to as diffraction cones), as well as the deficiency cones, emanate from the same irradiated small crystal volume. If the crystal is thick and of low absorption, namely, beryllium, the diffraction conics will have a large width, as shown in Fig. 3, since each point along the path of the

WE|SSMAN N ON STRUCTUR E-SENSITIVE PROPERTI ES

7.~ead d~o~'+ " " + - "

)/" "

90"ehkl

+

sheet

~ +pe,:mer,

\~\,,

\'\ \\ \\

film

(+0/I -I

/

Iraphy

"+,,

\',

--.-_-- .

FIG. 3-Schematic diagram illustrating the origin of deficiency and diffraction conics from the selected area of the specimen.

incident beam passing through the crystal functions as a vertex of a diffraction cone. Strain inhomogeneities caused by dislocations will be spread out over the diffraction conics and, therefore, it is the diffraction conics which are being used to obtain X-ray topographs. In contrast to the diffraction conics, the deficiency conics are sharp, since the vertex of the absorption cone is the X-ray point source. Consequently, the sharp lines of the deficiency conics are being used for the analysis of the X-ray line profiles. Before imaging the defect structure by X-ray topography, the divergent incident beam has to be transformed into a nearly parallel beam. This is accomplished by translating the specimen away from the X-ray source. The translation must be performed along the region of interest in the deficiency pattern, for only then are the identical diffraction conditions maintained. The technique of specimen translation, using a wire grid to preserve the area of interest and employing an aperture to convert the divergent beam into a parallel beam, has been described in detail [8]. Regions of special interest for analysis of the deficiency pattern are the intersections of several (hkl) lines. Such intersections pertain to a conic section which is common to the corresponding intersecting (hkl) planes. If the crystal is subjected to deformation, the line profiles will be sensitively changed. Microdensitometric measurements of the profiles carried out in the immediate vicinity of the intersection of the deficiency pattern may yield valuable information concerning the anisotropic deformation behavior of the crystal. Such information was obtained from

10

METALLOGRAPHY

compressive and tensile deformation of beryllium [9,10]. The corresponding topographs are obtained from the imaging of the intersection in the diffraction pattern and constitute the basis of selected area X-ray topography. Such topography affords a visualization of the defect structure of the crystal area pertaining to the corresponding line profile analysis. To establish a correlation between the defect structure analyzed by the X-ray method and that disclosed by TEM, a thin lead sheet with a hole 1 mm in diameter is attached to the entrance surface of the specimen, as shown in Fig. 3. TEM foils are prepared after the completion of the X-ray selected area studies by cutting a 2.5-mm disk centered around the hole [10]. The X-ray transmission method applied to the study of compressive deformation of beryllium crystals showed that inhomogeneous lattice rotation and basal plane bending resulted from the interaction of basal slip dislocations with columnar subgrain boundaries, a development that leads to bend plane splitting [12]. Correlation to TEM studies showed that the formation of cell walls and subgrain boundaries resulted from the interaction of slip dislocations with ingrown dislocations lying on the basal plane [8].

Lattice Distortions and Fracture in Brittle Crystals Disclosed by Anomalous Transmission of X-Rays (Borrmann Effect) When brittle crystals are subjected to mechanical deformation they form microplastic regions which confine large regions of locked-in elastic strains. These strains find ultimate relief either in brittle fracture, as recent deformation studies of silicon have shown [13], or they may develop microcracks, as in low-temperature deformation of tungsten and germanium crystals [14]. Such highly localized lattice defects can be disclosed sensitively by applying the technique of anomalous transmission (AT) of X-rays (Borrmann effect), which is based on the dynamical interaction of X-rays inside of nearly perfect crystals [15-17]. The observation of AT is indicative of a high degree of lattice perfection (dislocation density < l0 s cm-2). If any atoms are displaced from their normal nodes, for example, as a result of the strain field of a dislocation, discontinuities of the anomalously intense lines will be observed on the film. The critical conditions for AT are being destroyed and normal absorption has set in. Using the experimental arrangement schematically shown in Fig. 4, the X-ray divergent beam method can be effectively employed for the study of lattice defects in thick, elastically strained crystals. It offers the advantage that it never "loses sight" of the elastically strained lattice planes, for if the Bragg angles are slightly changed, some rays of the divergent beam will still be in reflecting position and an AT pattern will still be recorded. Furthermore, compared to the parallel beam method, the exposure times for obtaining AT patterns are five to ten times shorter. Figure 5 shows an AT pattern of a germanium crystal with the specimen kept stationary. If now the synchronized specimen and film translation is employed as shown in Fig. 4, one obtains a topographic mapping of the lattice perfection of the crystal. Thus, if adjacent

WEISSMANN ON STRUCTURE-SENSITIVE PROPERTIES

,

0

11

~x-Rt~v source{io~,)

FILM

/

t~I

0

FIG. 4-Experimental arrangement for obtaining AT patterns by the divergent beam

method.

FIG. 5-,4 T divergent beam pattern of unstrained germanium. areas exhibit such a high degree of lattice perfection that AT patterns can be obtained, the pattern of Fig. 5 will continuously broaden, as the specimen surface is traversed by the beam, and an AT pattern such as that shown in Fig. 6a is obtained. When the crystal, placed between the knife edges of the bending fixture, as shown in Fig. 8, was elastically bent short of fracture, the AT pattern shown in Fig. 6b was changed significantly. In agreement with the

12

METALLOGRAPHY

FIG. 6 - A T o f germanium, scanned area 5.5 x 1.75 mrn2; (a) undeformed, (b) bent, e = 0.5 percent. Note nonreflecting area.

theory of Penning and Polder [18], the reflections pertaining to the crystallographic planes, either parallel or perpendicular to the direction of the bending axis (DBA), remained unaltered in extent and intensity, while those pertaining to planes inclined at oblique angles to the DBA were considerably shortened. Focusing our attention now on the unaltered reflections parallel to DBA, it will be observed that certain areas in Fig. 6b indicated by arrows exhibited an absence of AT when the crystal was scanned. However, upon releasing the bending moment, the diffraction pattern assumed its original appearance of equal-sized segments and intensity as displayed in Fig. 6a. The nonreflecting areas of Fig. 6b, indicating localized lattice defects in the crystal, could not be caused by the generation of glissile dislocations, since these constitute irreversible plastic sites and the observed effect was shown to be perfectly reversible. To elucidate the nature of the defect structure responsible for the absence of AT on bending, the crystal was first translated to the position where the nonreflecting areas were observed and subsequently, the incident divergent beam was transformed into a parallel beam by increasing the distance between specimen and X-ray source and by placing a slit aperture in front of the specimen. Thus Fig. 7 was obtained.

WEISSMANN ON STRUCTURE-SENSITIVE PROPERTIES

13

FIG. 7 - A T pattern o f germanium by parallel beam method disclosing microcracks. Crystal bent, e = 0.5 percent. The beam conversion technique employed is quite analogous to that previously discussed, when the topographic information had to be extracted from the diffraction conics of the pseudo-Kossel pattern. In the latter case, however, the imaging of the defect structure was accomplished by employing the parallel beam transmission technique with normal absorption (Lang topography [19]), while in the former case the imaging was obtained by parallel beam AT. It is interesting to note that with copper K a radiation and a specimen thickness of 1 mm the exposure time took 20 h for the parallel beam technique, while the preceding AT scan obtained by the divergent beam technique (Fig. 6) required only 2 h. Thus, the divergent beam scan functioned as an efficient surveyor of the defect structure which, once its location was established, could be subsequently imaged by converting the incident divergent beam to a parallel beam. The imaged defect structure shown in Fig. 7 could be identified as microcracks which upon bending of the crystal expanded, and which, together with their concomitant elastic strain field, destroyed the AT locally. After removal of the bending moment the microcracks contracted again, relaxing the elastic strains and restoring the AT pattern. Following Cottrell [20], one may

14

METALLOGRAPHY

visualize the elastic microcrack as an ellipticaUy shaped discontinuity in a homogeneous elastic solid, equivalent to a continuous array of dislocations [20], which under the influence of a suitable external force can be made to expand, and on removal of this force to contract.

Instrumentation of X-Ray Divergent Beam Combination Method Since the various aspects of the X-ray divergent beam method have been discussed for the transmission and back-reflection applications, and since it was shown that they work synergistically when used in combination, it may be useful to discuss the instrumentation which enables one to apply this combination method in practice. Figure 8a offers a front-side view of the instrumentation employed, and with the back-reflection film holder removed, represents essentially all the experimental features necessary for the various transmission techniques. Figure 8b offers a back view of the instrumentation and, with the back-reflection holder I in place, depicts the experimental

(1) Back-reflection film holder, (2) transmission film holder, (3) specimen holder with bending device, (4) divergent beam source, (5) vertical scan mechanism, (6) horizontal scan mechanism, (7) scan control, (8) electron gun housing, (9) electromagnetic lens, (10) X-ray tube, (11) optical bench with precision scale. FIG. 8-Experimental arrangement o f combination method based on divergent beam techniques. (a) Transmission, and pa) transmission and back reflection.

WEISSMANN ON STRUCTURE-SENSITIVE PROPERTIES

15

FIG. 8-(Continued.) arrangement for the combined transmission and back-reflection divergent beam method. The sleeve design of the film holder 1 permits removal of the film holder from the horizontal X-ray tube 10 without any disturbance to the location of the specimen under investigation. Thus, back-reflection and transmission patterns can be obtained simultaneously. Various specimen holders and deformation devices were designed for different types of deformation, for example, tensile, compression, and bending devices, and a device of the latter type is shown as item 3 in Figs. 8a and 8b.

16

METALLOGRAPHY

The electrons generated by the electron gun 8 held at high potential are being accelerated and focused by an electromagnetic lens 9 to the tip of the tube 4. The tip, held at ground potential, contains the target foil which represents the source of the emergent, divergent X-ray beam. Tip and target may be replaced easily if a different characteristic radiation is required, a The horizontal scan mechanism 5 and the vertical scan mechanism 6 provide for the coupled X-Y translation of specimen and film. Such translation motion is particularly useful if the sites of lattice defects are to be located by selected area topography, using either the normal or the AT technique. The optical bench with precision scale 11 is provided with precision spacers which facilitate the ray-tracing technique in back reflection. It will be recalled that upon this tracing technique rest the precision measurements of the lattice parameters and of the interatomic spacings, and hence, it represents an important experimental link to the stress-strain analysis of the crystal. Study of Fracture Mechanism in Crystals by a Combination Method Based on X-Ray Pendell6sung Fringes, Double-Crystal Diffractometry, TEM, and SEM

[13,22] A useful combination method was recently developed which, applied to the study of fracture of crystals, is capable of detecting and assessing the microplastic regions and elastic stress fields generated by the crack tip [13]. The novel approach takes advantage of the disturbance of pendellosung fringes (PF) obtained by X-ray transmission topography of wedge-shaped crystals. This method is highly sensitive, since PF similar to AT are based on the dynamical interaction of the X-ray wave fields inside the crystal. Dynamical interaction occurs between the primary and secondary beams analogous to that which takes place between a pair of coupled pendulums whose frequencies are nearly equal. The two wave fields interact to give a beat effect, whereby the primary beam has all the energy at the surface, but at a certain depth this state of affairs is reversed, and the secondary beam has all the energy, and so the alternation goes on. The PF, therefore, can be obtained only from crystals of varying thickness, and it is for this reason that wedgeshaped crystals are being investigated. The depth of the layer, called extinction distance, at which complete alternation takes place, is the greater the more nearly the velocities of the two waves approach. The extinction distance ~g is measured along the normal to the X-ray entrance surface of the crystal. The aspect of PF patterns most relevant to the fracture study is the fact that very small lattice disturbances have a profound effect on the dynamical interaction of the wave fields and, therefore, change drastically the PF pattern. From the viewpoint of the materials scientist, the fracture study of silicon 3 An X-ray tube of this type and a diffraction unit (Microflex) are commercially produced by the Rigaku-DenkiCo., Tokyo, Japan.

WEISSMANN ON STRUCTURE-SENSITIVE PROPERTIES

17

crystals offers several attractive features. First of all,. these crystals can be obtained nearly dislocation-free. Secondly, at elevated temperatures (650~ to 1000~ silicon deforms plastically like a metal. It undergoes a ductile-brittle transition at lower temperature and is totally brittle at room temperature. Moreover, any lattice distortions introduced at elevated temperatures become frozen in at room temperature, so that the details of the defect structure which has been outlined by the preceding X-ray investigation can then be disclosed by TEM without fear that the defect structure was altered by the thinning process during specimen preparation. Lastly, it should be pointed up that ~g is inversely proportional to the structure factor F of the reflecting ( h k l ) plane, and, via F, it is also inversely related to the atomic number Z of the crystal. It is expected, therefore, that perfect wedge-shaped crystals of low Z values, namely, silicon, will yield a well-resolved PF pattern. Such crystal specimens into which a V-notch was introduced were prepared for tensile deformation. The crystal surface had a (211) orientation with the [01i-] direction parallel to the tensile axis. Figure 9 shows a Lang projection topograph of a notched specimen deformed in tension at 800~ The nominal stress, On, was 1.6 kg mm -~ and the strain rate e w a s 5.9 x 10 -s s-1 9o n is defined by F [ A , where F is the applied load and A the measured minimum cross-sectional area. This topograph was obtained by directing a finely collimated X-ray beam onto the crystal, which was placed approximately at right angles to the incoming beam so that the set of transverse (111) planes satisfied the conditions of Bragg reflections. The transmitted reflected beam was recorded on the film, while the transmitted primary beam was prevented by a stationary screen from striking the film. The crystal holder and film holder, being mechanically coupled, were moved to and fro during the exposure. Figure 9 may serve to illustrate the type of i~aformation which can be

FIG. 9 - X - r a y topograph o f notched silicon crystal deformed & tension at 800~ 1.6 kg m m -2, e = 5.9 x 10 -5 s-1 .

t7n =

18

METALLOGRAPHY

obtained from PF patterns in fracture studies. The regions of plastic zones, such as those associated with the notch N or those generated from the specimen surface opposite to the notch, are characterized by the total destruction of the PF pattern. They appear as black or white (out of contrast) areas on the topograph. The regions of elastic strains are characterized by the bending of PF and by the systematic narrowing of the fringe spacing when the plastic zone is approached. Although the distortions of the PF patterns are quite reminiscent of the optical fringe contours encountered in photoelastic stress analysis of materials transparent to light, it must be remembered that the distortions of the PF pattern result from displacements on an atomic scale and depend only on the transparency of perfect crystals to X-rays. To assess the dislocation density of the plastic zone quantitatively, the PF technique is supplemented by the method of double-crystal diffractometry. Thus, the primary beam is first reflected from a perfect silicon crystal and the monochromatized radiation is directed towards that area on the test crystal which is outlined by the destruction of the PF pattern. The reflecting power of the test crystal is measured by rotating ("rocking") the crystal through its angular range of reflection. The width /3 at half maximum of the obtained rocking curve is a measure of the crystal perfection and can be related to the excess dislocation density of one sign D by [21] D =/3/3bt, where b is the magnitude of the Burgers vector and t the linear size parameter of the crystal area investigated. Thus, the PF technique functions as a "guiding eye" to locate the microplastic zone which is to be quantitatively evaluated by the double-crystal diffractometer method. The sensitivity of detecting microplastic zones can be gaged from the fact that a lattice misalignment /3 of 45 s of arc was sufficient to destroy the PF pattern which corresponds to a dislocation density of ~ lO s cm -2. The dislocation structure of the microplastic zone itself can be disclosed by TEM, and Fig. 10 shows such a zone in proximity to the crack tip. Thus, one arrives again at a combination method in which each component part, namely, PF technique, double-crystal diffractometry, and TEM, fulfills a synergistic function. Using this combination method, the zones of plastic deformation and elastic strains in notched silicon crystals were mapped out as a function of applied stress and deformation temperature [22]. It could be shown that at the low deformation temperature of 600~ silicon fractured in a brittle manner. Fracture was initiated by a small plastic zone at the crack tip, sensitively disclosed by the destruction of PF in the vicinity of the tip, and the crack propagated along one of the (111) planes without any lateral formation of a plastic zone. At more elevated deformation temperatures, namely, 700~ other microplastic zones were generated besides those associated with the notch root. These microplastic zones, similar to those shown in Fig. 9, were strain-hardened zones which constrained regions of residual elastic strains. The formation of these strain-hardened microplastic zones and the associated regions of locked-in elastic strains explain the occurrence of the notch-brittle

WEISSMANN ON STRUCTURE-SENSITIVE PROPERTIES

19

FIG. lO-Electron micrograph of dislocation structure in silicon near crack tip. transition observed around 650~ It was observed that for unnotched speci. mens, the fracture stress at 600"C was 15 kg m m -2 and the yield stress at 700~ was 8 kg mm -2 . Such a decline in stress level with increasing deformation temperature is, of course, expected. For notched specimens, however, this trend was reversed. The fracture stress at 600"C was ~ 3 kg mm -2 , while the yield stress at 700"C was virtually identical with that of the unnotched specimen. At the low deformation temperature of 600~ the microplastic zones other than the minute one associated with the notch root were absent, and all the elastic strain energy found catastrophic release at a critical stress level, resulting in cleavage fracture. At the elevated deformation temperature of ?00*C the strain-hardened microplastic zones, which were generated principally at the specimen surface, formed effective boundaries of pockets into which residual elastic strains were locked (Fig. 9). Consequently, both the yield and fracture stresses increased considerably. At still higher deformation temperatures, both the yield and fracture stresses declined because the dislocations in the plastic zones could rearrange themselves into a configuration of lower energy by cross-slip and climb, and thereby decrease the efficiency of the barrier effect in confining residual elastic strains [22]. The efficiency of the plastic zones in constraining regions of locked-in, residual elastic strains, and the mechanism by which the elastic strains relaxed, were studied by controlled annealing experiments following the tensile deformation. It could be shown by X-ray topography that the relaxation of the locked-in elastic strains occurred through the formation of dislocation loops at the boundaries of the plastic regions. These loops interacted so as to form a relaxed threedimensional dislocation configuration, with the sum of the Burgers vector tending toward zero (hexagonal network). Thus, relaxation of the residual elastic strains occurred by spreading of microplastic zones.

20

METALLOGRAPHY

The formation of microplastic regions and the concomitant onset of ductility in notched silicon crystals at 650~ revealed by the destruction of PF, could be also correlated to interesting results obtained by scanning electron microscopy (SEM). Examination of the fracture surface by SEM disclosed at this deformation temperature the appearance of the first cleavage steps, an indication that dislocations had been intersected and, consequently, that microplastic regions were formed [22]. The results obtained by applying the combination method to the study of silicon crystals underlined generally the importance of microplasticity in deformation prgcesses. In particular they emphasized the impact of microplasticity on the fracture mechanism, for it could be shown [22] that the extent of the plastic region associated with the crack tip was invariably 10 to 15 times larger than that predicted on the basis of approximations used in continuum mechanics. Discussion-Interplay of Component Techniques in Combination Methods In correlating the visualization of lattice defects, as disclosed by X-ray topography, to quantitative X-ray diffraction analyses of materials such as the stress-strain, line profile, and rocking curve analyses, one may well have achieved a research goal that can give one added confidence in interpreting the behavior of structure-sensitive properties. Nevertheless, it is important to realize that in transversing the material X-rays average out details of the defect structure, and hence, X-ray topography is capable of disclosing only relatively gross features of the defect structure. These may include subgrain formation, slip and deformation bands-in short, long-range cooperative phenomena of dislocation interaction. Individual dislocations can be disclosed only when the dislocation density is very low and even in the most favorable cases this would restrict the observation to only the initial stages of deformation of a material. TEM, on the other hand, is capable of revealing details of the defect structure such as the individual dislocations and dislocation networks shown in Fig. 10. Such resolution exceeds the resolving power of X-ray topography by many orders of magnitude. The principal disadvantage of TEM, however, lies in the fact that only small specimen areas of about 10~2 or in some cases 100/12 can be studied. Because of this limited restriction of the field of view, it is frequently difficult for TEM to discern the essential features and parameters that determine and govern the structure-sensitive properties of the material. The TEM method "sees frequently too much," and to be most effective it requires another research tool for guidance. In the combination methods of structural analysis described in this paper such guidance is provided by X-ray topography. X-ray topography, however, should be employed not only for quick and effective location of a defect structure, but principally for locating and discerning structural features of importance to the process under study. For example, in the deformation study of beryllium [8-10], X-ray topography was employed on the intersection of the deficiency conics pertaining to the basal, prismatic, and pyramidal planes of beryllium. Consequently, the anise-

WEISSMANN ON STRUCTURE-SENSITIVE PROPERTIES

21

tropic deformation behavior of a small, selected, irradiated crystal volume could be analyzed by studying the deformation (compression and tension) response of the different (hkl) planes. Subsequently, the complementary TEM study was able to focus attention on the mechanism of dislocation interaction which was responsible for the formation of the cell structure observed by X-ray topography and was able to disclose the development of the cell structure leading up to fracture [10]. Another example may serve to illustrate the synergistic interplay of the component techniques to make the application of the combination method most effective. In the fracture study of silicon [13,22], the PF topography was capable of distinguishing zones of elastic residual strains from those containing plastic deformation. The latter were analyzed by double-crystal diffractometry and the details of the dislocation configuration, particularly in the vicinity of the notch root, were revealed subsequently by TEM. Corroborative evidence that microplastic zones were formed in notched silicon at the ductile-brittle transition temperature of about 650~ was obtained from the observations of fine cleavage steps on the fracture surface disclosed by SEM. It appears quite safe to predict that SEM, with its recent extension of X-ray analysis by energy dispersion, will play an increasingly important role in the future developments of the combination methods. The greatest sensitivity in locating lattice defects by X-ray topography is achieved when the topographic method is based on phase contrast rather than on reflectivity contrast. Topography based on phase contrast, such as AT contrast (Figs. 6 and 7), or PF contrast (Fig. 9), requires crystals of very low dislocation density. There is ample evidence, however, that besides the transistor type of crystals there exists a host of other crystals of technological importance, namely, crystals used in laser operation, which might be suitable candidates for such study. Conclusions

Combination methods of structural analysis were developed which make it possible to correlate the visualization of lattice defects, disclosed by X-ray topography and TEM, to quantitative X-ray diffraction analysis of structuresensitive properties of materials. Depending on the information desired, the quantitative diffraction analysis may consist of: (a) line profile analysis, such as was performed in the analysis of deficiency conics of divergent beam patterns of beryllium, (b) rocking curve analysis, as was carried out in the analysis of microplastic regions in fracture studies of silicon, and (c) stress-strain analyses based on strain measurements of back-reflection divergent beam patterns. These were applied to precipitation-hardened and ordered alloys and to neutron-irradiated materials. It was shown that the topographic disclosure of lattice defects was most effective when the techniques of X-ray topography and TEM were so employed as to complement each other. Owing to its larger field of view, X-ray

22

METALLOGRAPHY

topography was capable of locating the importanL gross topographical features, the details of which were studied subsequently b y TEM. It was shown that certain isolated lattice defects, such as microcracks, microplastic regions, or zones containing residual elastic strains, were most effectively revealed when X-ray topographic methods were employed which are based on phase contrast. Thus, the lattice defects were disclosed by the disturbance o f AT or PF. SEM o f fracture surfaces played an important part in assessing the early formation o f microplastic regions.

Acknowledgment The partial support of this work b y the Rutgers Research Council is gratefully acknowledged. References [1] Imura, T., Weissmann, S., and Slade, J.J., Acta Crystallographica, Vol. 15, No. 8, Aug. 1962, pp. 786-793. [2] Ellis, T., Nanni, L.F., Shrier, A., Weissmann, S., Padawer, G.E., and Hosakawa, N., Journal of Applied Physics, Vol. 35, No. 11, Nov. 1964, pp. 3364-3373. [3] Slade, J.J., Weissmann, S., Nakajima, K., and Hirabayashi, M., Journal of Applied Physics, Vol. 35, No. 11, Nov. 1964, pp. 3373-3385. [4] Nakajima, K., Slade, J.J., and Weissmann, S., Transactions Quarterly, American Society for Metals, Vol. 58, No. 1, March 1965, pp. 14-29. [5] Weissmann, S., Imura, T., Nakajima, K., and Wisnewski, S.E., Journal of the Physical Society of Japan, Vol. 18, Supplement III, March 1963, pp. 179-188. [6] Weissmann, S. and Shrier, A. in The Science, Technology and Application of Titanium, R. Jaffee and N. Promisel, Eds., Pergamon Press, New York, 1970, pp. 441-451. [7] Newman, B.A. and Weissmann, S., Journal of Applied Crystallography, Vol. 1, Part 3, Sept. 1968, pp. 139-145. [8] Glass, H.L. and Weissmann, S., Journal of Applied Crystallography, Vol. 2, 1969, pp. 200-209. [9] Glass, H.L. and Weissmann, S., Metallurgical Transactions, Vol. 2, 1971, pp. 2865-2873. [10] Kannan, V.C. and Weissmann, S., Journal of Applied Physics, Vol. 42, 197I, pp. 2632-2638. [11] Weissmann, S. and Kannan, V.C., Journal of Materials, Vol. 7, No. 3, Sept. 1972, pp. 279-285. [12] Stroh, A.N., Philosophical Magazine, Vol. 3, 1958, p. 597. [13] Weissmann, S., Tsunekawa, Y., and Karman, V.C., Metallurgical Transactions, Vol. 4, Jan. 1973, pp. 376-377. [14] Weissmann, S. and Kalman, Z., Philosophical Magazine, Vol. 15, No. 135, March 1967, pp. 539-547. [15] Borrmann, G., Physikalische Zeitschrift, VoL 42, No. 9/10, July 1941, pp. 157-162. [16] yon Laue, M., Acta Crystallographica, VoI. 2, 1949, pp. t06-113. [17} yon Laue, M., RiSntgenstrahlen Interferenzen, Akademische Verlagsgesetlschaft, Frankfurt/Main, 1960. [18] Penning, P. and Polder, D., Philips Research Reports, Vol. 16, No. 10, Oct. 1961, pp. 419-440. [19] Lang, A.R., Journal of Applied Physics, Vol. 29, No. 3, March 1958, pp. 597-598. [20] Cottrell, A.H., Fracture, Wiley, New York, 1959, p. 2. [21] Hirsch, P.B. in Progress in Metal Physics, Pergamon Press, New York, Vol. 6, 1956, p. 282, [22] Tsunekawa, Y. and Weissmann, S., "Importance of Microplasticity in Fracture of Silicon Crystals," paper accepted by Metallurgical Transactions.

Leo Zwell I

X- Ray Diffraction - A Versatile, Quantitative, and Rapid Technique of Metal Iography

Zwell, Leo, "X-Ray Diffraction-A Versatile, Quantitative and Rapid Technique of Metallography," Metallography-A Practical Tool for Correlating the Structure and Properties of Materials, ASTM STP 557, American Society for Testing and Materials, 1974, pp. 23--42. ABSTRACI': X-ray diffraction is used to delineate the structure of materials, their chemical and phase analyses, grain and domain sizes, internal strain (stress), texture, imperfections, homogeneity, etc. In this paper, the practicality of the methods is emphasized; diffractometer techniques can be simple, quantitative, and rapid, and together with film techniques, permit examination of a wide range of materials. Examples are given of the characterization of structure by X-ray diffraction techniques and of the applications of the results in such different investigations as mechanical and physical properties of solid solutions, recrystallization of steel, pore structure of carbons, creep properties, surface stresses, and transformation of austenite to bainite. KEY WORDS: X-ray diffraction, metallography, crystallography, vreparation, lattice parameters, carbon, mechanical properties, recovery, crystatlite ize, texture REFERENCE:

In the 1948 edition of "Metals H a n d b o o k " published b y the American Society for Metals (ASM), metallography is defined as "the science concerning the constitution and structure of metals and alloys as revealed by the microscope." In the 1961 edition, metaUography is "the science dealing with the constitution and structure of metals and alloys as revealed by the unaided eye or b y such tools as low-powered magnification, optical microscope, electron microscope and diffraction or X-ray techniques." Now, in 1973, the field of metallography has been broadened to cover much more than metals and alloys-metallography is a tool for correlating the structure and properties of materials. In 1965, ASTM Committee E-4 defined metallography as "that branch o f science which relates to the constitution and structure, and their relation to the properties of metals and alloys." As the old saying goes, metallography is what metallographers do. One might say that the structure o f a material is known when the following characteristics have been determined: the quantitative chemical elemental analysis; the existing phases and their relative amounts; the sizes, shapes, and distribution of these phases; and finally, additional factors such as texture, internal strain, ordering parameter, and homogeneity. The list grows with t i m e - t r u l y a large number o f features required to describe structure. X-ray analysis comprising the three aspects o f radiography, fluorescence, and I Consultant, Swarthmore, Pa. 19081. 23 Copyright 91974 by ASTM Intemational

www.astm.org

24

METALLOGRAPHY

diffraction is certainly the most versatile method available because almost all aspects of structure can be investigated. These subjects have been described in the literature often and well, both in breadth and in depth. The purpose of this paper is to demonstrate the practicality of X-ray diffraction in revealing the structure of materials and the correlation of the results to other properties of interest. Examples have been chosen to emphasize the diverse nature of problems which can be investigated with commercial or easily assembled equipment. Most of the work to be described has been performed at the United States Steel Corporation Research Center. In the natural course of events, the studies have been cooperative in nature. The joint efforts of many co-workers, too numerous to name individually, are acknowledged with much appreciation.

Specimen Preparation The ease, simplicity, rapidity, and versatility of specimen preparation merit emphasis. In the Debye-Scherrer camera technique, the aim is to center the specimen in the X-ray beam and rotate it so that many orientations and grains are seen. The three common ways of placing a specimen in this camera are: (1) to coat the outside of a thin nonreflecting fiber with the specimen using a binder such as Canada balsam, (2) to place powder inside a thin-walled capillary, and (3) to shape the specimen into a suitable rod. This can be done for solids by cutting the specimen and subjecting it to chemical attack. In other instances, a mixture of powdered material and a binder (balsam or collodion, for example) is either rolled into a rod or placed in a tube and extruded. The advantages of the camera method are that all diffraction peaks are recorded at the same time, that very small amounts of sample can be used, and a tremendous range of time of exposure is possible. Other cameras are available, like the Guinier-deWolff type which gives higher resolution and permits the simultaneous exposure of four powder patterns. For examination on a diffractometer, the main requirement is that the specimen be fiat-so fiat sheets or ground and polished specimens can be examined without further preparation. Powders can be examined quickly by dusting them onto double-coated transparent tape mounted on a glass slide. Slurries of powder and a binder (lacquer, collodion, or cement) can be placed on a glass slide and warmed until the volatile part of the binder has evaporated. Pieces of material can be placed on a slide either with the tape or with a binder. Powders can also be placed in a recess in a nondiffracting plate flush with the surface of the plate. Finally, samples can be mounted in bakelite, epoxy resin, or other mounting material commercially available, and then made flat for examination on the diffractometer. One advantage of X-ray diffraction analysis, especially in camera techniques, is that small specimens can be examined. Particles have been separated on the basis of appearance, density, or magnetic or chemical property, and identification obtained therefrom.

ZWELL ON X-RAY DIFFRACTION

25

Elemental Analysis The chemical analysis of materials is determined by X-ray techniques in several ways: (1) most accurately, by measuring characteristic X,rays produced by electron bombardment as in the electron microprobe or by X-ray bombardment as in X-ray spectrometers, (2) by determining lattice parameters where the change of lattice parameter with composition is known, and (3) by using the absorptivities of the elements (because of density or absorption edge) as in microradiography. Microradiography has the great advantages of simplicity of procedure, low cost, and examination of the specimen in bulk. The drawbacks are serious or more investigators would be using the technique (low resolution and a long time required for specimen preparation and exposure). Microradiography is still being used to show segregation within specimens, but microprobe analysis has practically taken over the field, for example, the recent study on solidification of high speed tool steel by Barkalow et al [1] .2 An example of the value of microradiography is its application to the investigation of surface defects produced during severe forming. Ridging is a defect caused by differences in the directional properties of sheets which arise from the nonrandomness of the orientations of the grains in the sheet. This condition of nonrandom orientation is called texture or preferred orientation. (Perhaps this paper should have been devoted mainly to a discussion of texture, because preferred orientation is a natural and ever present result of the working of materials and X-ray diffraction is the best way to determine texture. Since the aim of the paper is to emphasize the versatility and practicality of X-ray diffraction, subjects which are handled relatively quickly and easily have been chosen.) At the United States Steel Corporation Research Laboratory, J.D. Defilippi and H.C. Chao [2] employed iron and chromium X-radiation to delineate a band-like segregation of chromium and molybdenum in hot-rolled- AISI Type 434 stainless steel (17Cr-lMo). Their thesis is that segregation of the elements in the ferrite and austenite phases may lead to retention of a harmful texture in the finished sheet. Because of selective absorptivity, chromium (and vanadium and titanium) will selectively absorb iron radiation; because of higher density, molybdenum will absorb both iron and chromium radiation more than the other elements in this steel. With the aid of a reference mark scribed on the surface, it was possible to take a light micrograph and then radiographs of the same area of a hot-rolled sheet ground and polished down to a thickness of 25.4 #m (1 mil). The results are shown in Fig. 1. The white areas in l b and l c represent regions of high absorptivity, chromium for iron radiation, and molybdenum for both iron and chromium radiations. The areas which are white in both radiographs indicate concentration of molybdenum; those areas white in the iron target radiograph and dark in the chromium 2 The italic numbers in brackets refer to the list of references appended to this paper.

FIG. l-Longitudinal section o f steel plate (a] light micrograph, (bJ radiograph by iron.Kot, (c] radiograph by chromium-K~. X101. Courtesy of Metallurgical Transactions, Ref. 2.

-1.
1 J 2 tn-1 l-a Sc/~r n and AC

=

C A

-

C'a >1 vr2 CA tn_l l-a Sc

(7b)

(N A - # 8 )

where CA = element composition of one element in the specimen, A/a and IVB = average number of X-ray counts of element A .for the specimen and the element continuum background on the specimen, tn-11-a = "student's" factor dependent on the confidence level 1-a (Table 2) and, n = number of repetitions. Ziebold [83] has shown that the analytical sensitivity for a 95 percent confidence level can be approximated by t A C = C a _ CA>>.

2.33

Ca (IrA

Equation 8 represents achieved when signals instrumental errors are about two times larger

an estimate from both disregarded. than oc, AC

Oc

(8)

-

of the maximum sensitivity that can be compositions have their own errors but Since the actual standard deviation (Sc) is is approximately twice that given in Eq 8.

GOLDSTEIN ON THE ELECTRON MICROPROBE

113

If/VA is much larger than NB, Eq 9 can be rewritten as A C = C A - C tA >t 2.33 Ca

(9)

and the analytical sensitivity that can be achieved is given as AC

__

2.33 x 102

(%)=

ca

(10)

xg- A

Shastry and Judd [84] investigated grain boundary solute segregation in an A1-6.86Zn-2.35Mg alloy which is susceptible to corrosion cracking. They found depletion or enrichment at the grain boundaries depending on the type of heat treatment and quench rates employed. They designed their experiments so'vahies of A C / C A (percent) for both zinc and magnesium were about 1 percent. In one case the relative change in concentration at the boundary was --~ 5 percent for both zinc and magnesium. To study olivine (FeMg)~ SiO4 compositional equilibration in large pallasite meteorites, olivine crystals from the opposite ends of several specimens ~ 50 cm apart were obtained [85]. Using Eq 7b at the 95 percent confidence limit, a sensitivity of ~ C / C A (percent) was about 1 percent. In all three meteorites, differences between the olivine crystals were less than this limit. As the elemental composition C A approaches 0.1 percent in EMP analysis, N A is no longer much larger than -NB- This composition range, below 0A percent is called the trace element analysis range. The analysis procedure now is to detect significant differences, between the specimen and the continuum background generated from the specimen. The detectability limit is governed by the minimum value of the difference "~A - NB which can be measured with statistical significance. Analogous to Eq 7a we have ~rA _ ~rB >t vr 2 tn_l 1-a Sc

(11)

,/n where S c is essentially the same for both the specimen and background measurement. For trace analysis, < 1000 ppm, the X-ray calibration curves (Eq 4) may be taken as a simple linear function. Therefore, C A , the unknown composition, can be related to 57A by the equation

cA __

-

C(A)

(la)

-

where /Vs and ]qBs = mean counts for the standard and standard background for element A , and

114

METALLOGRAPHY

C(A) = percent of element A in the standard. Using Eq 11 and 12, the detectability limit CDL = CA is [86]

CDL=

C(A) (Ns - NSB)

4"2 (tn. 1 l-a) Sc

(13)

~

The precision in a trace element analysis is equal to CA[CoL and approaches -+ 100 percent as CA approaches CDL. Ziebold [83] has shown the trace element sensitivity to be

CDL ~ 3.29a/(n 7"I R) w2

(14)

where time of each measurement taken, number of repetitions of each measurement, I = pure element counting rate, R = peak/background ratio of the pure element (it is the ratio of the counting rate of the pure element to the background counting rate of the pure element), and a = relation of composition and intensity of element A through the Ziebold and Ogilvie [87] empirical relation. To illustrate the use of this relation, the following values were used for calculating the detectability limit for germanium in iron meteorites [88]. The operating conditions were: high voltage, 35 kV specimen current, 0.2 uA I = 150000 counts/s R = 200 r = lOOs n = 16 a = 1 Using these numbers, CDL >~ 15 ppm. The actual detectability limit after calculation of S c and Eq 12 was 20 ppm. Equation 14 is very useful for determining the operating conditions for trace analysis before the actual data are taken. Therefore, to do trace element analysis one needs to employ long counting times, high peak intensities, and a high peak to background ratio (R). Because of instrumental drift, and specimen contamination, a practical limit on the counting time is 15 to 30 min. The peak intensities can be raised by increasing the beam current. However, beam currents over 0.2 ttA tend to heat the specimen locally and increase the size of the electron beam. Unfortunately, the peak to background ratio cannot be reduced below a certain limit since continuum X-ray radiation is always present and very small peaks from trace elements are difficult to separate statistically from the background continuum. Trace element measurements have been made by various authors. Heidel T

--

n

=

GOLDSTEIN ON THE ELECTRON MICROPROBE

115

[89] measured COL for metallic elements in a silicate glass. Using +3 % above background as -~.4 - /VB, he found a detectability limit of 150 to 350 ppm for 20 kV, 2 x 10-SA specimen current and 10-s counting times. If 2 x 10-TA specimen current and lO0-s counting times were used, a detectability limit of 15 to 35 ppm could have been achieved. Buseck and Goldstein [85] made trace element measurements of manganese, nickel, titanium, and calcium in olivine crystals. Operating at 30 kV, 2 x 10-~A specimen current and taking four 100-s counts per crystal, the detectability limits according to Eq 13 were 40 ppm for manganese, 20 ppm for nickel, 10 ppm for titanium, and 15 ppm for calcium. In practice, therefore, it is very difficult to obtain measurements below a detectability limit of 10 ppm. Trace element measurements are almost always made in the EMP using X-ray crystal spectrometers. The peak to background ratio (R) is quite high ( > t00) and at the specimen currents typically used, the peak intensity is also quite high, >104 to l0 s counts/s from the pure elements. The background intensity (NB) must be obtained to determine (CA) the unknown composition, Eq 12. As discussed the previous section of this paper, with careful usage, the background intensity can be obtained by going off the wavelength peak on the specimen itself. It would be of great advantage to obtain trace analysis measurements at low beam currents, ~< 10-9 A, where it might be possible to have a smaller X-ray excitation area. The solid state detector might be a logical instrument to use in this case. The peak intensity (/) is high at these specimen currents although the peak to background ratio (R) is much poorer than that obtained with the crystal spectrometer. According to Eq 12, Ct)L would approach 100 ppm in the best cases. However, detectability limits of .,

I-.4

1 180.5

1. t820

I t825

I 1830 Energy,

I 1835

e840

t845

eV

FIG. 26a-Silicon K-X-ray bands from elemental silicon, Si02 and SiO.

GOLDSTEIN ON THE ELECTRON MICROPROBE

131

Oxygen K

tO t.-4

SiOz t

I

518

l

I

522

i

Enlrgy,

I

526

I

I

550

i

eV

FIG. 26b-Oxygen K-band for SiO and Si02 (C~luartz). trums are virtually identical indicating again that the condensed phase SiO consists of a variable mixture of silicon and SiO2. Other studies have characterized films containing nitrogen [128]. In addition, combined EMP and ellipsometric study of thin SiO2 films on silicon enabled data to be obtained on contamination films as well as the mass thickness and uniformity of the thin film [129]. Other examples of soft X-ray application to materials characterization have been reported in the literature [130-132] and give support for the use of this technique to microprobe analysis. Acknowledgments The author wishes to acknowledge Jesearch support from NASA under grant number NGR 39-007-043 and from NSF grant number GA 15349.

References [1] Castaing, R., Advances in Electronics and Electron Physics, L. Marton, Ed., Academic Press, New York, 1960, p. 317. [2] Heinrich, K.F.J., Applied Spectroscopy, Vol. 22, 1968, p. 395. [3] Beaman, D.R. and Isasi, J.A., Materials Research and Standards, Vol. 11, No. 11, 1971, p. 8. [4] Pease, R.F.W. and Nixon, W.C., Journal of Scientific Instruments, Vol. 42, 1965, p. 81. [5] Duncumb, P. and Shields, P.K., British Journal of Applied Physics, Vol. 14, 1963, p. 617. |6] Kanaya, K. and Okayama, S., Journal of Physics D, Applied Physics, Vol. 5, 1972, p. 43.

132

[7] [8] [9]

[10] [11 ] [12] [13] [14]

[151 [16]

METALLOGRAPHY

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[21] Jaklevic, J.M. and Goulding, F.S. in Proceedings, Sixth National Conference on Electron Probe Analysis, Pittsburgh, July 1971, paper No. 1.

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[31 ] Bence, A.E. and Albee, A.L., Journal o f Geology, Vol. 76, 1968, p. 382. [32] Myklebust, R.L. and Heinrich, K.F.J. in Energy Dispersion X-ray Analysis: X-ray and Electron Probe Analysis, ASTM STP 485, American Society for Testing and Materials, 1971, p. 232.

[33] Russ, J.C. in Energy Dispersion X-ray Analysis: X-ray and Electron Probe Analysis, ASTM STP 485, American Society for Testing and Materials, 1971, p. 154.

[34] Henoc, J., Heinrich, K.F.J., and Myklebust, R., TechnicalNote, National Bureau of Standards, 1972~ in press.

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[67] Wittry, D.B., Applied Physics Letters, Vol. 8, 1966, p. 142. [68] Muir, M.D., Grant, P.R., Hubbard, G., and Mundell, J. in Scanning Electron Microscopy/1971, Proceedings, Fourth Annual Scanning Electron Microscope Symposium, April 1971, liT Research Institute, Chicago, Ill., p. 403.

[69] Kniseley, R.N., Laabs, F.C., and Fassel, V.A., Analytical Chemistry, Vol. 41, 1969, p. 50.

[70] Smith, J.P. in Transactions, Third National Conference on Electron Microprobe Analysis, Chicago, IU., July 1968, Paper No. 38.

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[961 D~rfler, G. and Russ, J.C. in Scanning Electron Microscopy/1970, Proceedings, Third Annual Scanning Electron Microscope Sympdsium, April 1970, liT Research Institute, Chicago, I!1., p. 67. [97] White, E.W., Johnson, G.G., and McKinstry, H.A. in Scanning Electron Microscopy/1968, Proceedings, First Annual Scanning Electron Microscope Symposium, April 1968, l i t Research Institute, Chicago, IlL, p. 95. [981 McMillan, R.E., Johnson, G.G., and White, E.W. in Scanning Electron Microscopy/1969, Proceedings, Second Annual Scanning Electron Microscope Symposium, April 1969, l i t Research Institute, Chicago, I11.,p. 439. [991 GSrz, H., White, E.W., McMillan, R.E., and Lebiedzik, J. in Proceedings, Fifth National Conference on Electron Probe Analysis, New York, July 1970, Paper No. 10. []001 Braggins, D.W., Gardner, G.M., and Gibbard, D.W. in Scanning Electron Microscopy/1971, Proceedings, Fourth Annual Scanning Electron Microscope Symposium, April 1971, liT Research Institute, Chicago, IlL, p. 393. [lO1 l Fisher, C. and Gibbard, D.W. in Proceedings, Sixth National Conference on Electron Probe Analysis, Pittsburgh, Pa., July 1971, Paper No. 54. [lO21 Duke, M.B. and Brett, R., Geological Survey Research, Vol. B101, 1965, p. 103. [1031 Fleetwood, M.J., Higginson, G.M., and Miller, G.P., British Journal of Applied Physics, Vol. 16, 1965, p. 645. [lO41 Ancey, M., Henry, G., Philibert, J., and Tixier, R. in lh'fth International Congress on )(.ray Optics and Microanalysis, Tiibingen, 1968, G. M6lienstedt and K.H. Gaukler, Eds., Springer-Verlag, Berlin, 1969, p. 509. []o51 Duncumb, P. in The Electron Microprobe, T.D. McKinley, K.F.J. Heinrich, and D.B. Wittry, Eds., Wiley, New York, 1966, p. 490. [lO61 Cooke, C.J. and Duncumb, P. in Fifth International Congress on X-ray Optics and Microanalysis, Th'bingen, 1968, G. M(fllenstedt and K.H. Gaukler, Eds., Springer-Verlag, Berlin, 1969, p. 245. [lO71 Cooke, C.J. and Openshaw, I.K. in Proceedings, Fourth National Conference on Electron Microprobe Analysis, Pasadena, Calif., July 1969, Paper No. 64. []o81 Ryder, P.L. and Jackel, G., Zutschrift fuer Metallkunde, Vol. 63, 1972, p. 187. [1091 Bolon, R.B. and Lifshin, E. in Scanning Electron Microscopy/1973, Proceedings, Sixth Annual Scanning Electron Microscope Symposium, April 1973, IIT Research Institute, Chicago, IlL, p. 287. []to] Curgenven, L. and Duncumb, P., "Tube Investments Research Laboratory Report No. 303," July 1971. [111] Jackson, M.R., Goldstein, J.I., and Kraft, R.W. in Proceedings, Sixth National Conference on Electron Microprobe Analysis, Pittsburgh, Pa., July 1971, Paper No. 22. [112] Reed, S.J.B. and Long, J.V.P. in X-ray Optics and X-ray Microanalysis, Third International Symposium, Stanford University, Stanford, Calif., 1962, H.H. Pattee, V.E. Cosslett, and A. Engstr~Sm, Eds., Academic Press, New York, 1963, p. 317. [1131 Goldstein, J.l. and Ogilvie, R.E. in X-ray Optics and Microanalysis, Fourth International Congress on X-ray Optics and Microanalysis, Orsay, 1965, R. Castaing, P. Deschamps, and J. Phflibert, Eds., Hermann, Paris, 1966, p. 594. II141 Maurice, F., Sequin, R., and Henoc, J. in X-ray Optics and Microanalysis, Fourth International Congress on X-ray Optics and Microanalysis, Orsay, 1965, R. Castaing, P. Deschamps, and J. Philibert, Eds., Hermann, Paris, 1966, p. 357. [115] Henoe, M.J., Maurice, F., and Zemskoff, A. in Fifth International Congress on X-ray Optics and Microanalysis, Tiibingen, 1968, G. Mtillenstedt and K.H. Gaukler, Eds., Springer-Verlag, Berlin, 1969, p. 187. []161 Rapperport, E.J. in Electron Probe Microanalysis, A.J. Tousimis and L. Marton, Eds., Academic Press, New York, 1969, p. 117. [1171 Gupta, P.K., Journal of Physics D: Applied Physics, Vol. 3, t970, p. 1919. il]81 Miyake, G.T. and Goldstein, J.l. to be published in Geochimica et Cosmochimica Acta, 1974. Miyake, G.T., "The Shock and Thermal History of Two Unusual Iron Meteorites," M.S. thesis, Lehigh University, 1973. [1191 Gilmour, J.B., Purdy, G.R., and Kirkaldy, J.S., Metallurgical Transactions, Vol. 3,

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[1201 Fischer, D.W. and Baun, W.L., Norelco Reporter, Vol. 14, 1967, p. 92. [121 ] Solomon, J.S. and Baun, W.L., Applied Spectroscopy, Vol. 25, 1971, p. 518. [1221 Colby, J.W., Wonsidler, D.R., and Androshuk, A. in Proceedings, Fourth National Conference on Electron Probe Analysis, Pasadena, Calif., July 1969, Paper No. 26. [1231 Colby, J.W. in Proceedings, Sixth International Conference on X-ray Optics and Microanalysis, G. Shinoda, K. Kohra and T. Ichiokawa, Eds., University of Tokyo Press, 1972, p. 247. [1241 Holliday, J.E., Norelco Reporter, Vol. 14, 1967, p. 84. [125] Krause, H.B., Savanick, G.A., and White, E.W., Journal o f the Electrochemical Society, Solid State Science, Vol. 177, 1970, p. 557. [1261 Baun, W.L and Solomon, J.S., Vacuum, Vol. 21, 1971, p. 165. [1271 White, E.W. and Roy, R., Solid State Communications, Vol. 2, 1964, p. 151. [1281 Colby, J.W. in Thin Film Dielectrics, F. Vratny, Ed., Electrochemical Society, New York, 1969, p. 491. [129] Knausenberger, W.H., Vedam, K., White, E.W., and Zeigler, W., Applied Physics Letters, Vol. 14, 1969, p. 43. I1301 Solomon, J.S. and Baun, W.L. in Proceedings, Seventh National Conference on Eiectron Probe Analysis, San Francisco, Calif., July 1972, Paper No. 1 I. [1311 Baun, W.L. and Solomon, J.S., "Technical Report AFML-TR-70-80," Air Force Materials Laboratory, 1970. [1321 Solomon, J.S. and Baun, W.L, "Technical Report AFML-TR-70-253," Air Force Materials Laboratory, 1970.

M.G.H. Wells 1 a n d J.M. Capenos 1

Transmission Electron Microscopy in Materials Research

REFERENCE: Wells, M.G.H. and Capenos, J.M., "Transmission Electron Micros-

copy in Materials Research," Metallography-A Practical Tool for Correlating the Structure and Properties of Materials, ASTM STP 557, American Society for Testing and Materials, 1974, pp. 137-168. ABSTRACT: This paper very briefly reviews the development of transmission electron microscopy (TEM) including instrumentation and specimen preparation techniques, and generally describes typical examples of the use of TEM today in the study and understanding of the structure of materials. New observation techniques such as energy loss analysis, dark field imaging, the weak beam technique, Kikuchi line analysis, and computer generation of dislocation images are discussed. In addition to forefront work, many illustrations are given where TEM has greatly contributed to the optimization of properties and general improvement of many commercially important materials. KEY WORDS: metallography, electron microscopy, energy loss analysis, electron diffraction, martensite, decomposition Twenty-three years ago, Subcommittee I 1 on Microscopy and Diffraction (Committee E 4 on Metallography) presented to the American Society o f Testing and Materials (ASTM) a report which chronicled the first systematic study o f steel structures using the electron microscope [1].2 A collection o f replica micrographs was presented showing details o f pearlite and martensitic structures which had never before been seen. This historic work served as a foundation and spur for the metals and materials research community as it unmistakably demonstrated the usefulness and potential of the electron microscope in structure studies at higher magnifications and resolutions than was previously possible. In fact, the full potential of the electron microscope was little understood at that time b y most workers and is only being realized today, 30 years after the appearance of the first commercial microscopes. In some respects, this has been extremely rapid progress. This paper will briefly review specimen preparation techniques and generally describe some typical examples of the use o f transmission electron microscopy (TEM) today, in the study and understanding of the structure of materials. Illustrations are given where the use of TEM has benefited technology b y helping to optimize properties and generally improve materials. t Technical director and staff microscopist, respectively, Crucible Materials Research Center, Colt Industries, Pittsburgh, Pa, 15230. 2 The italic numbers in brackets refer to the list of references appended to this paper.

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Copyright 91974 by ASTM Intemational

www.astm.org

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METALLOGRAPHY

Most of the recent advances in TEM have come about as a result of increased resolution of the instrument, improved specimen preparation techniques, and further sophistication in image analysis. Greatly increased magnification and resolving power of the TEM over those of the optical microscope were, of course, the main features of electron microscopy exploited during the early years; materials and techniques for surface replica preparations improved rapidly, and a number of convenient, reliable surface replica techniques were developed which afforded good high magnification images of specimen topography. Figure 1, a typical shadowed surface replica from a polished and etched martensitic steel specimen, illustrates the fine detail reproduced by this technique.

FIG. 1-Shadowed surface replica electron micrograph o f polished and etched martensitic T-410 stainless steel. The size and distribution o f carbides within the martensite can be clearly seen. The extraction replica technique, first described by Fisher [2], made possible the direct examination and identification by electron diffraction of inclusions and precipitate phases removed from bulk specimens by the replicating process. Figure 2 illustrates extraction replica preparations of (a) coarse M:z3C6 grain boundary precipitates from T-446 stainless steel and (b) fine intragranular nickel titanium (Ni3Ti) precipitates from an 18Ni maraging steel.

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FIG. 2-Extraction replica electron micrographs, (a) M23C6 grain boundary precipitates and the corresponding diffraction pattern from T-446 stainless steel and (b) ultrafine NiaTi precipitates from 18Ni maraging steel.

140

METALLOGRAPHY

Direct examination of thin metal foils, first accomplished by Heidenrich [3], gained popularity in the mid-1950's with the development of reproducible electrolytic thinning techniques. In 1956, Hirsch et al [4] and Bollman [5] published the first detailed studies of thin foil preparation and examination. Figure 3 illustrates the variety of details seen in a thin foil specimen of T-410 stainless steel heated at 1400~ for 2 h. This micrograph was prepared as part of a study of tempering reactions in this commercially important stainless steel [6]. Details of all of these techniques have been given in several excellent reviews [7-9].

FIG. 3-Thin foil electron micrograph o f T-410 stainless steel heated 2 h at 1400~ Note the variety o f substructural detail revealed by this technique,

In this period, the use of selected area diffraction (SAD) to determine the structure, orientation, and orientation relationships of metal foils was rapidly~ being developed. Researchers at the forefront of this field were advocating that a diffraction pattern be taken each time a micrograph was taken to gain the maximum information from the specimen. Thomas [10] helped to bring fundamentals to a large number of newcomers to the field. The kinematical theory of electron diffraction contrast had been developing for many years, and the more comprehensive dynamical theory of contrast was developed about this time. This theory, reviewed in detail by Hirsch et al [11], has proved invaluable in interpreting TEM images.

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Instrument Design Improvements Instrument design improvements over the past decade have resulted in a number of very sophisticated electron microscopes offering a combination of high performance, versatility, and ease of operation. Resolutions of the order of 5 to 10 .~ units are routinely obtained with most newer instruments using conventional imaging techniques. The double condenser lens system, now standard equipment on most instruments, permits a wide range of illumination conditions as well as better penetration of thin foil specimens. Other basic design improvements and additions include beam (gun) tilting devices for high resolution clark field studies, refined electromagnetic stigmators for better astigmatism correction, specimen anticontamination devices, high performance automatic vacuum systems, improved airlocking of various sections of the column, and greatly improved, high stability, solid state electronic circuitry. In addition to these basic instrument design improvements, a variety of accessories are available which further extend the versatility of the TEM. Of particular interest to the materials scientist are the special stages and specimen holders permitting tilt, rotation, heating, cooling, and tension testing of specimens in the microscope. Recording and display capabilities are extended by optional video tape recorder attachments and TV monitors. Most recently, X-ray analyzer attachments have become available permitting both wavelength and energy dispersive chemical analysis of microareas of electron microscope specimens.

New Observation Techniques Recent developments and improvements in observation techniques in electron microscopy include energy loss analysis, dark field imaging, and the weak beam technique, among others. These techniques, coupled with advances in the knowledge of diffraction theory, have greatly expanded the use of TEM in materials research. When electrons pass through specimens in the electron microscope they lose energy. These electrons have energy distributions that are characteristic of the element(s) comprising the specimen. Knowledge of this phenomenon has prompted a number of workers to develop energy analyzers to obtain a measure of the chemical composition of extremely small regions. These analyzers show the energy spectrum of transmitted electrons after they pass through a narrow slit beneath the specimen. Klemperer [12] has reviewed the development work up to 1965, and, more recently, Curtis and Silcox [13] have described a Wien-type focusing spectrometer for energy loss analysis in an electron microscope. However, not a great deal of experimental data has yet been obtained with this technique. Ever since the first electron microscopes became available, work has continued to improve their resolving power by design improvements. However, commensurately with instrument improvements, new techniques have been continually devised to utilize the improved resolving power. Menter [14] first resolved individual lattice planes using the (20]-) planes of platinum phthalo-

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cyanine with a spacing of 11.9 A. A high density of platinum ions along those planes provides higher electron scattering and image formation results from a recombination of the direct beam and the 20]- diffracted beam. An example of lattice imaging is shown in Fig. 4, in which lattice planes in a pyrophyllite crystal with a spacing of 4.45 A are deafly resolved [15]. Progress has

FIG.

4-Pyrophyllite crystal showing 4.45 A resolution of lattice planes [15].

continued to be rapid to the point where Hugo and Phillips [16] have resolved the 110 atomic planes of tungsten having a spacing of 2.23 A. Recently, Hashimoto [17] has been able to obtain an image of individual atoms. Thorium atoms in specimens of thorium-benzene tetracarboxylic acid supported on a graphite crystal were observed in dark field used to minimize image interference from the supporting material. Of course, the principal reason for wanting improvements in resolving power is to progressively study the very fine structure and substructure of materials. This high resolution is necessary for the examination of precipitate particles, but, in general, has not proved necessary for the study of dislocations. Dislocations may be imaged in the electron microscope when the crystal is set close to a Bragg reflecting angle. For most metals, dislocation images produced in this manner are of the order of 80 to 100 A wide, and a vast amount of analysis of dislocation configuration, interaction, movement, etc., has been done using this method (examples are given later in the paper). Recently, however, the weak beam technique has been used to obtain dislocation images an order of magnitude smaller than those produced under normal conditions. In the weak beam technique, which was first effectively

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t43

developed by Cockayne et al [18], a high resolution dark field micrograph is obtained by setting the crystal to an operating vector (g) which is far removed from the Bragg condition. Only the region near the dislocation core, where the planes are bent locally into the reflecting position, contribute to the image contrast. As pointed out by Hirsch [19], the method is suitable for accurate determination of the width of dissociated dislocations because the width of the individual images is very small. Figure 5 from Hirsch shows the effectiveness of this technique to more clearly define dislocations. Perhaps the major drawback to the weak beam technique is that rather time-consuming and tedious procedures are necessary to obtain the micrographs.

FIG. 5-(a) Strong beam and (b) weak beam images o f dislocation array made with the 220 reflection in deformed silicon. (Micrographs by LL.F" Ray and D.J.H. Cockayne, Courtesy o f P.B. Hirsch, [19].) Another useful technique becoming more widely used in electron microscopy is Kikuchi line analysis. Kikuchi lines, named after their discoverer [20], are formed by electron diffraction. An electron beam on entering a crystal specimen interacts with the atoms and is scattered inelasticaUy and incoherently. These electrons may then be rescattered coherently when Bragg's law is satisfied for a particular set of reflecting planes. Cones of radiation are then emitted which intersect the screen in hyperbolae. However, since the wavelength of electrons is very small, the Kikuchi lines in the image are very nearly straight. Although Kikuchi lines are present in thin crystals, they are only observed in thicker foils when the Kikuchi cone is sufficiently intense. In addition, the foil must be generally quite free of internal strains, such as a

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high dislocation density or elastic buckling, or the Kikuchi lines will be too diffuse to be readily observed. Thomas [10,21] has given a good account of the geometric formation of Kikuchi patterns which is adequate for most purposes. As Thomas points out, "The Kikuchi origin is fixed in the crystal so that the crystal is tilted, the cones sweep across the pattern as if rigidly "fixed" to the specimen. Thus, the Kikuchi pattern is extremely useful in determining the precise orientation, as well as for calibrating tilt angles etc . . . . Furthermore, the Kikuchi pattern represents the traces of all reflecting planes in the crystal and can thus be directly compared to the appropriate stereographic projection." [21 ]. Thus, Kikuchi line analysis may be used in orientation determinations and the study of phase transformations [22], as well as in the indexing of diffraction patterns. This analytical method has been discussed by several authors [23-26]. An example of a Kikuchi map is given in Fig. 6, in which a composite pattern (many individual exposures) made from hexagonal close packed (hcp) crystals of silver aluminum (Ag2AI) is shown together with the indexed schematic [24]. In a precise study of orientation relations using Kikuchi analysis, a good double-tilting stage is essential. Since Howie and Whelan [27] introduced the two-beam approximation of electron diffraction, there have been many calculations of the theoretical electron microscope images of various defects in thin foils. For dislocations the results are usually presented as a profile showing the variation of intensity along a line crossing the dislocation image. Head [28] has pointed out that the theoretical profiles are often mentally compared with the visual image or micrograph, and that a more valuable approach would be to present the theoretical images as pictures rather than as profiles. By computer integration of the Howie-Whelan differential equations describing image formation in the electron microscope and a suitable printout, various simple dislocations images have been generated. A more comprehensive discussion of such image formation has recently been given [29]. Figure 7 is of a dislocation dipole where the individual dislocations are not really resolved. This example shows the advantage of a pictorial rather than a graphical presentation of the theoretical prediction. While not a great deal of application of this technique has yet been used, it does appear that computer generation and pictorial presentation of defects observed in thin foils in the electron microscope will considerably increase our knowledge of the subject.

Use of TEM in Structure-Property Relationships For most materials scientists and engineers, electron microscopy is a tool, albeit a very powerful tool, to be used in developing an understanding of structure-property relationships. Electron microscopy has greatly helped workers to improve and optimize the properties of engineering materials. As discussed previously, TEM has shown a very, very rapid growth in the last ten years because of its unique value in this area. Of particular importance is the

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FIG. 6-(a) Composite Kikuchi map of hcp Ag2AI, C/a = 1.588, showing all reciprocal lattice sections and traces lying within 35 ~ of the [0001] zone axis. (b) Fully indexed, distortion-free schematic o f (a) [24].

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FIG. 7-(a) Experimental micrograph of a dislocation dipole in nickel compared with (b) a set o f computed intensity profiles and (c) a matching theoretical micrograph. The profiles and the theoretical micrograph were computed using the data corresponding to the particular circumstances o f (a) [29].

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improvement in microscopes themselves and the advances in the theory of diffraction contrast. This has led to both better images and a much greater understanding in the interpretation of images. In this section we will show some examples where TEM has greatly contributed to our understanding of structures and their relationships with properties. In particular, the technique has proved useful in the study of phase transformation and deformation mechanisms. The development of superalloys has contributed greatly to man's technological advance in the last 30 years. The precipitation hardenable alloys really began during the early years of World War II with the development of the Nimonic nickel-base superalloys [30]. These creep resistant, high temperature materials designed for the early jet engines have been greatly improved in recent years and are essential to the aerospace industry today. Some early studies of the nickel-aluminum system had established by X-ray the presence of the Ni3A1 phase [31]. However, although these nickel-base alloys were used extensively in this period it was not until 1950 in a study of the constitution of the nickel-chromium-aluminum system that the precipitate responsible for hardening in these alloys was identified by X-ray diffraction as ordered 7 x [32]. Electron metallography was first used about that time and helped in the early identification of 3,1 [33]. Since that time, electron microscopy has played a large part in the further understanding and development of these alloys. For example, it is now known that the precipitate particles, which are very small and cannot be resolved by normal optical microscopy, are coherent and coplanar with the face centered cubic (fcc) 3' austenitic matrix. In addition, TEM of thin foils has helped in the elucidation of deformation mechanisms. An excellent summary of studies of 71 particles and the nature of dislocation interactions with these particles is given by Obtak and Kear [34]. To ensure correct interpretation of the complex microstructures, a thorough understanding of the dynamical theory of electron diffraction is necessary. An example of the cuboidal 71 particles in the commercial \ alloy Udimet 700 is shown in Fig. 8a. The misfit between the coherent particles and the matrix (for example, the difference in lattice parameters of the two phases) is only ~ 0.1 percent and little or no strain contrast is observed. The 7/71 misfit is much greater for the alloy in Fig. 8b (Ni-8.2A1-3.3Cb), and results in considerable strain contrast. The TEM has greatly helped in the development of dislocation theory because dislocations can be readily observed directly, and thus has also contributed immeasureably to our understanding of deformation mechanisms. In addition to dislocation configurations, the Burgers vector of dislocations may be determined by TEM, and the nature of stacking faults and the measurement of stacking fault energy may be determined. Lattice dislocations are out of contrast in a bright field image when the dot product of the operating vector (in a two-beam image) and the Burgers vector of the dislocation is equal to zero. Thus, by two different operating vectors in which the dislocation is out of contrast, the Burgers vector may be obtained.

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FIG. 8-(a) Cuboid coherent particles o f l~[l in a "y (austenite) matrix in Udimet 700 showing virtually no strain contrast, (b) "y particles in a Ni-8.2AI-3.3Cb alloy showing the strain contrast resulting from a much larger ~/~1 lattice mismatch [34]. The conditions for determining the Burgers vector of partial dislocation are different, but may also be calculated [11]. An example of the varying visibility of partial dislocations in graphite as a function of the operating vector is shown in Fig. 9 due to Amelinckx and Delavignette [35]. In Fig. 9a, the extended and contracted stacking fault nodes bounded by partials can be readily observed. In the other three rnicrographs each of the three sets of partial dislocations are respectively out of contrast when different strong operating reflections are imaged, An esti-

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FIG. 9-(a) Extended and contracted stacking fault nodes in graphite. The nodes are bounded by partial dislocations which are respectively out of contrast in (b), (c), and (d) taken with three different operating reflections [35]. mate of the stacking fault energy may be made by measuring the radius of curvature of the partials bounding an extended node. Howie and Swann [36] used this technique to measure stacking fault energy in a number of copper and silver-based alloys. Stacking faults in crystals may be made visible in the TEM under suitable diffraction conditions. In bright field imaging the stacking fault appears as fringes as shown in Fig. lOa [34]. In dark field the fringes at the extreme edge on one side (for example, at one edge of the thin foil) of the fault change contrast. With a knowledge of the operating reflection, the nature of the stacking fault can be determined. In Fig. 10b, for example, extrinsic stacking faults in MAR-M200 superalloy can be seen, where the fringe at the bottom is now white in dark field compared with the black fringe seen in the bright field micrograph (Fig. 10a). The methods of TEM are particularly suited to the study of alloy systems exhibiting precipitation reactions. Age hardening was first discovered serendipitously more than 60 years ago in an aluminum alloy, and although a considerable amount of work was done, subsequently, many years passed

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FIG. lO-(a) Bright field micrograph o f stacking faults in the su_peralloy MAR M200, Co) dark field micrograph using the operating reflection g --- 111 reveals the extrinsic nature o f the faults [34]. before the hardening mechanism was clarified by Guinier, Preston, and Wassermann, principally by single crystal X-ray studies. In 1954, Hardy and Heal [37] published a review of precipitation, including a discussion of the structure of systems undergoing precipitation hardening mainly determined by X-ray diffraction techniques. Soon after this, as noted previously, electron metaUographic techniques [4,5] began to be developed, and with the direct study of precipitates and dislocation interactions in thin foils, began to greatly increase our understand-

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ing of the mechanism of age hardening. As pointed out by Kelly and Nicholson [38] in an extensive review, the main advantage of electron microscopy is that it directly reveals the microstructure of an alloy, that is, information on the number, size, shape, distribution, and orientation relationships of precipitate particles can be obtained. It should be stressed at this point that while TEM is an extremely useful tool in the study of material structures, other techniques (such as X-ray diffraction and electrical resistivity measurements) should often be used in conjunction with TEM for a complete characterization of the microsl;ructure. Much work has been done on the dislocation configurations resulting from the annihilation of quenched-in vacancies, since these have been shown to play an important part in the nucleation process. Figure 11 is an example showing dislocation loops in polycrystalline pure aluminum quenched from 600"C [39]. The metallography of precipitation in an aluminum-silver alloy has been

FIG. 11-TEM of pure aluminum quenched from 600~ showing dislocation loops formed by the condensation of vacancies [39]. studied extensively by Nicholson and Nutting [40]. Figure 12 shows the structure in the overaged condition in which precipitates of 71 have spread over almost the whole crystal, although Guinier-Preston (GP) zones are still present between the 71 platelets. Many aspects of the nucleation and growth of GP zones, 71 and 7 in various aluminum-based alloys, with and without

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FIG. 12-Electron micrograph o f a thin foil of Al-4.4Ag alloy, water quenched from 525"C, and aged I00 days at IO0~ showing the extensive heterogeneous precipitates of 3/1. Some GP zones, ~ 200 ,~ diameter are still present in regions such as H which are isolated from 3/1 particles [40]. small additions of other elements, have been studied with TEM and the literature is voluminous on this subject. Thus, TEM has greatly enhanced our understanding of precipitation in aluminum alloys which, of course, are widely used commercially. There are also many other systems that exhibit age hardening, and TEM has helped in the solution of problems and the development of new alloys in steels. Strain aging and quench aging of iron-carbon alloys while being useful, in some cases have caused problems in the steel industry. These phenomena have been studied for many years, often producing conflicting results. However, with the use of TEM the two stage precipitation of e-carbide and cementite could be followed directly and correlated with other observations [41]. An example of e-carbide precipitation in an Fe-0.035C alloy is shown in Fig. 13. In this micrograph the beginnings of cementite precipitation may be observed. Extensive studies have also been made of precipitation reactions in the iron-nitrogen system, and of dislocation-precipitate interactions in these systems [42]. In all these studies, SAD was used extensively to determine the habit planes of precipitate particles. More recently, there has been considerable activity on titanium-based alloys stimulated by the increased usage and demands of the aerospace industry. In many high-strength, heat-treatable t3-phase titanium alloys, the to phase may precipitate under certain conditions [43]. Considerable hardening also accom-

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FIG. 13-e-carbide particles precipitated on 100 planes in a q[~enc~ed and aged Fe-O.035C alloy. Note the beginning of cementite precipitation on ~110~ planes (see arrow). panied by embrittlement occurs as a result of co formation, so that the presence of this phase is generally undesirable. However, knowledge concerning the kinetics of precipitation, morphology, nucleation, etc., are essential to the design of new alloys and optimum heat treatments of current titanium grades. While much was known about the co phase from studies using other techniques, principally X-ray diffraction, TEM provided a method to directly "see" the particles [441. The co phase forms on {111} /3 planes of the body centered cubic (bcc) matrix with four variants. In studies of co, dark field techniques are very useful, so that only variants may be observed independently. In studies of phase transformations [45] in Beta III, athermal co formed during the water quench may be seen in Fig. 14. The total volume percentage of all four variants in this case is less than 10 percent, co may reach quite a high volume percentage in some instances, for example, in Fig. 15 only one variant is shown in the dark field micrograph, and the total volume percentage of co is of the ord'er of 50 percent or more. Another example of the use of dark field microscopy is shown in Fig. 16, where the ot precipitation on the dislocations may be clearly seen [45]. The study and understanding of martensitic transformations have far reaching practical implications because the resulting structures form the basis for hardened steels and are important in many nonferrous alloy systems. The existence of martensite has been known for many years, and although martensite was known to form by a shear mechanism (in which each atom moves less than one atomic distance during transformation) details of the fine structure remained obscured up to about 1960. In the 1950's, the phenomenological generalized theories were published that describe the crystallography of the transformation with respect to the parent and martensite phases [46,47]. Perhaps the first TEM work was that of Pitsch [48], who

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FIG. 14~-Bright field electron micrograph showing the four variants of ~Oprecipitation on ~IlI ~ planes in Ti-ll.SMo-6Zr-4.5Sn (Beta III) alloy. Courtesy of J.C. Williams 1451: " studied transformed thin foils of iron-carbon, iron-nitrogen, and iron-nickel alloys. The orientation relationship he found was quite different from that found in bulk material. Evidently, the transformation constraints are less than in a massive specimen. At this point it seems appropriate to emphasize that special care should be exercised in the interpretation of thin foil experiments made directly in the electron microscope. Because of the much smaller restraint in a thin foil, the nature and kinetics of transformations can be considerably changed, particularly those of strain-induced transformations such as occur in martensite. Kelly and Nutting [49] then showed that martensite in steels occurs in two main forms. In low carbon steels, the structure consists of needles containing a high dislocation density (Fig. 17), while in higher carbon and more highly alloyed materials the martensite occurs as plates which are internally twinned on a fine scale (see Fig. 18) [50]. Since that time there has been a considerable amount of work using TEM on the crystallography of various martensites, particularly by Wayman et al [51]. As mentioned previously, much work has also been done on nonferrous alloys exhibiting martensitic transformations. Some alloys with very small hysteresis between the forward and reverse transformations exhibit "rubberlike" behavior and thermoelastic properties. One interesting transformation occurs in the so-called "Marmem" alloys, in which a specimen (apparently) plastically deformed at a lower temperature will revert to its original shape on

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FIG. 15-Dark fieM electron micrograph showing one o f the o.~ phase variants in Beta

IIL In this case the total volume percentage of 6o is high {